Magma V2.19-8 Wed Aug 21 2013 00:03:20 on localhost [Seed = 1074146890] Type ? for help. Type -D to quit. Loading file "K13n1756__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K13n1756 geometric_solution 11.60521806 oriented_manifold CS_known -0.0000000000000001 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 4 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 -1 0 -1 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.511309607628 0.348387048865 0 5 6 3 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.328791051725 0.620461952633 3 0 5 7 0321 0132 1302 0132 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -2 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.483151252151 0.532834422260 2 8 1 0 0321 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 -1 0 1 0 -1 -2 -1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.239434561626 0.761043134385 9 7 0 10 0132 2031 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.452638135744 0.913950139273 2 1 11 12 2031 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.013193243122 0.516899039983 9 10 12 1 3120 1023 2031 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.411891550165 1.673688838875 4 8 2 12 1302 0213 0132 2310 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.273292837407 0.624859013942 9 3 7 11 1023 0132 0213 0321 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 1 -1 -1 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.760555460990 0.463790880836 4 8 11 6 0132 1023 1023 3120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 -1 1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.532958714311 1.165043049499 6 11 4 12 1023 1023 0132 2031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.263804143841 0.658940403805 10 8 9 5 1023 0321 1023 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.050928852021 1.377380245236 7 10 5 6 3201 1302 0132 1302 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.209860706681 0.832097410899 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_0101_10'], 'c_1001_10' : d['c_0011_7'], 'c_1001_12' : d['c_0110_10'], 'c_1001_5' : d['c_1001_3'], 'c_1001_4' : d['c_0101_12'], 'c_1001_7' : d['c_1001_0'], 'c_1001_6' : d['c_0101_10'], 'c_1001_1' : d['c_0110_10'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_3'], 'c_1001_2' : d['c_0101_12'], 'c_1001_9' : d['c_0011_7'], 'c_1001_8' : d['c_1001_0'], 'c_1010_12' : d['c_1010_12'], 'c_1010_11' : d['c_1001_3'], 'c_1010_10' : d['c_0011_12'], 's_3_11' : d['1'], 's_3_10' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0011_7'], 'c_0101_10' : d['c_0101_10'], 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : negation(d['1']), 's_2_3' : d['1'], 's_2_4' : d['1'], 's_2_5' : d['1'], 's_2_6' : d['1'], 's_2_7' : d['1'], 's_2_12' : d['1'], 's_2_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : d['1'], 's_0_7' : d['1'], 's_0_4' : d['1'], 's_0_5' : negation(d['1']), 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : negation(d['1']), 's_0_1' : negation(d['1']), 'c_0011_11' : d['c_0011_10'], 'c_1100_8' : d['c_0101_10'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_0101_6'], 'c_1100_4' : negation(d['c_1010_12']), 'c_1100_7' : d['c_0011_12'], 'c_1100_6' : negation(d['c_1010_12']), 'c_1100_1' : negation(d['c_1010_12']), 'c_1100_0' : negation(d['c_1010_12']), 'c_1100_3' : negation(d['c_1010_12']), 'c_1100_2' : d['c_0011_12'], 's_0_10' : d['1'], 'c_1100_9' : negation(d['c_0101_6']), 'c_1100_11' : d['c_0101_6'], 'c_1100_10' : negation(d['c_1010_12']), 's_0_11' : d['1'], 'c_1010_7' : d['c_0101_10'], 'c_1010_6' : d['c_0110_10'], 'c_1010_5' : d['c_0110_10'], 'c_1010_4' : d['c_0011_7'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_3'], 'c_1010_0' : d['c_0101_12'], 'c_1010_9' : negation(d['c_0011_10']), 'c_1010_8' : d['c_1001_3'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_7' : d['1'], 's_3_6' : d['1'], 's_3_9' : d['1'], 's_3_8' : d['1'], 'c_1100_12' : d['c_0101_6'], 's_1_7' : d['1'], 's_1_6' : d['1'], 's_1_5' : negation(d['1']), 's_1_4' : d['1'], 's_1_3' : d['1'], 's_1_2' : negation(d['1']), 's_1_1' : negation(d['1']), 's_1_0' : negation(d['1']), 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : negation(d['c_0011_3']), 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_3'], 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : d['c_0011_10'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_3'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0011_12'], 'c_0110_10' : d['c_0110_10'], 'c_0110_12' : negation(d['c_0101_10']), 'c_0101_12' : d['c_0101_12'], 'c_0101_7' : negation(d['c_0011_3']), 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0011_12'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0011_0'], 'c_0101_2' : negation(d['c_0011_0']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0011_0'], 'c_0101_9' : d['c_0101_10'], 'c_0101_8' : d['c_0011_7'], 'c_0011_10' : d['c_0011_10'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_1'], 'c_0110_8' : negation(d['c_0011_10']), 'c_0110_1' : d['c_0011_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0011_0'], 'c_0110_2' : negation(d['c_0011_3']), 'c_0110_5' : d['c_0101_12'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : negation(d['c_0101_12']), 'c_0110_6' : d['c_0101_1']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0011_3, c_0011_7, c_0101_1, c_0101_10, c_0101_12, c_0101_6, c_0110_10, c_1001_0, c_1001_3, c_1010_12 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 21 Groebner basis: [ t - 50835526704346689031989048518821786618241573/9193396015100438338980\ 1878376602615113054575*c_1010_12^20 - 162534510976272910570255356305457130885768197/919339601510043833898\ 01878376602615113054575*c_1010_12^19 + 114913278625927303282483907590827601263116849/919339601510043833898\ 01878376602615113054575*c_1010_12^18 + 1063573834561666996421719750671610869489714027/91933960151004383389\ 801878376602615113054575*c_1010_12^17 + 1824457350443493990926624216311366106303916/13343100167054337211872\ 5512883312939206175*c_1010_12^16 - 1770202092569877069972605649664950714152377911/91933960151004383389\ 801878376602615113054575*c_1010_12^15 - 1155850546528778735760289330409118112535756733/18386792030200876677\ 960375675320523022610915*c_1010_12^14 - 3249818939520340303448782582180317158064493268/91933960151004383389\ 801878376602615113054575*c_1010_12^13 + 7802265190140224224592530927475710553787769036/91933960151004383389\ 801878376602615113054575*c_1010_12^12 + 12514105737203473545125386185588155416226923758/9193396015100438338\ 9801878376602615113054575*c_1010_12^11 + 17947625603936012235152324327395894670769667/1734603021717063837543\ 431667483068209680275*c_1010_12^10 - 1980551184944720354452702892979473257471345919/18386792030200876677\ 960375675320523022610915*c_1010_12^9 - 248364263823574495779184536423774841017809520/367735840604017533559\ 2075135064104604522183*c_1010_12^8 + 2946864071402099005935466541735663320991530033/91933960151004383389\ 801878376602615113054575*c_1010_12^7 - 3796257761660791510521194750761824531883008191/91933960151004383389\ 801878376602615113054575*c_1010_12^6 - 44058526979538262941430256401128349744744577952/9193396015100438338\ 9801878376602615113054575*c_1010_12^5 + 34133621494547515528832753753640311389267623078/9193396015100438338\ 9801878376602615113054575*c_1010_12^4 + 83941441758907369364909644801153732793491958393/9193396015100438338\ 9801878376602615113054575*c_1010_12^3 - 53812209606583749950126430384704007374587563757/9193396015100438338\ 9801878376602615113054575*c_1010_12^2 - 47029589742427349451371168947886550805701844428/9193396015100438338\ 9801878376602615113054575*c_1010_12 + 31306710728590929175816454389498774113314649931/9193396015100438338\ 9801878376602615113054575, c_0011_0 - 1, c_0011_10 + 44114285636809238660890066/55375796333535513299868115*c_101\ 0_12^20 + 138255801482628493076694839/55375796333535513299868115*c_\ 1010_12^19 - 107746285793346687184712023/55375796333535513299868115\ *c_1010_12^18 - 915838612292818143525885179/55375796333535513299868\ 115*c_1010_12^17 - 1039177843248152669036698193/5537579633353551329\ 9868115*c_1010_12^16 + 1597493162618691308740604372/553757963335355\ 13299868115*c_1010_12^15 + 988049634362310357404362054/110751592667\ 07102659973623*c_1010_12^14 + 2564307998929017992894814336/55375796\ 333535513299868115*c_1010_12^13 - 6955008528660060226856499077/5537\ 5796333535513299868115*c_1010_12^12 - 10608595513587276725329794026/55375796333535513299868115*c_1010_12^\ 11 - 359619833595855095507358647/55375796333535513299868115*c_1010_\ 12^10 + 1753617298109569653098643249/11075159266707102659973623*c_1\ 010_12^9 + 1056884088550675656702787391/11075159266707102659973623*\ c_1010_12^8 - 2644094848660067269161643096/553757963335355132998681\ 15*c_1010_12^7 + 3388430637886582155043499352/553757963335355132998\ 68115*c_1010_12^6 + 37835366858780490099952373999/55375796333535513\ 299868115*c_1010_12^5 - 32003352121834371332489666406/5537579633353\ 5513299868115*c_1010_12^4 - 70731957269576654860442522301/553757963\ 33535513299868115*c_1010_12^3 + 48729819937125818536547846409/55375\ 796333535513299868115*c_1010_12^2 + 38690638281959316023108520906/55375796333535513299868115*c_1010_12 - 26848833521415650371906862237/55375796333535513299868115, c_0011_12 + 5443485620475116406802346/55375796333535513299868115*c_1010\ _12^20 + 17446472895397629149933394/55375796333535513299868115*c_10\ 10_12^19 - 12300927217807057408883543/55375796333535513299868115*c_\ 1010_12^18 - 115598548347913432131078639/55375796333535513299868115\ *c_1010_12^17 - 140322870751285540644794163/55375796333535513299868\ 115*c_1010_12^16 + 187636408039685765379448517/55375796333535513299\ 868115*c_1010_12^15 + 128500173148803352682929947/11075159266707102\ 659973623*c_1010_12^14 + 400370715593899460864404006/55375796333535\ 513299868115*c_1010_12^13 - 818225111360114566405879702/55375796333\ 535513299868115*c_1010_12^12 - 1442428739528607156557947751/5537579\ 6333535513299868115*c_1010_12^11 - 286927291567462737549737342/55375796333535513299868115*c_1010_12^10 + 197728074997583748720534042/11075159266707102659973623*c_1010_12^\ 9 + 161575680347285925145355466/11075159266707102659973623*c_1010_1\ 2^8 - 83182706048821436906215926/55375796333535513299868115*c_1010_\ 12^7 + 582426978010730517672605092/55375796333535513299868115*c_101\ 0_12^6 + 4844845415986678164483703544/55375796333535513299868115*c_\ 1010_12^5 - 3491126148500266306672968006/55375796333535513299868115\ *c_1010_12^4 - 9133827069189953232065292926/55375796333535513299868\ 115*c_1010_12^3 + 4723081629398112305020014939/55375796333535513299\ 868115*c_1010_12^2 + 4827677707968181680415301611/55375796333535513\ 299868115*c_1010_12 - 2620443056806988985230290582/5537579633353551\ 3299868115, c_0011_3 - 19695238976922975647021401/55375796333535513299868115*c_1010\ _12^20 - 60894029779347486796920949/55375796333535513299868115*c_10\ 10_12^19 + 51706507704975469129425748/55375796333535513299868115*c_\ 1010_12^18 + 411277715762409732254606434/55375796333535513299868115\ *c_1010_12^17 + 449860143471978446577887053/55375796333535513299868\ 115*c_1010_12^16 - 750022184339854278687432987/55375796333535513299\ 868115*c_1010_12^15 - 444371474992221705601738048/11075159266707102\ 659973623*c_1010_12^14 - 1073952345263841058483875976/5537579633353\ 5513299868115*c_1010_12^13 + 3241690989782727009203211702/553757963\ 33535513299868115*c_1010_12^12 + 4780471299838752297000994061/55375\ 796333535513299868115*c_1010_12^11 + 22581138799246631602337097/55375796333535513299868115*c_1010_12^10 - 819420039101282337756879434/11075159266707102659973623*c_1010_12^9 - 486892059054033810432175945/11075159266707102659973623*c_1010_12^8 + 1183292906352636632402426176/55375796333535513299868115*c_1010_12^7 - 1555722195743358880116287802/55375796333535513299868115*c_1010_12\ ^6 - 16881927342508733310696450969/55375796333535513299868115*c_101\ 0_12^5 + 15004001669352122370238043491/55375796333535513299868115*c\ _1010_12^4 + 31864282629721740567539701856/553757963335355132998681\ 15*c_1010_12^3 - 22642994300341113874639443144/55375796333535513299\ 868115*c_1010_12^2 - 17499350023591201523929671416/5537579633353551\ 3299868115*c_1010_12 + 12344250843005051809236111332/55375796333535\ 513299868115, c_0011_7 - 83839395390666622793938439/55375796333535513299868115*c_1010\ _12^20 - 266336646162512195926787551/55375796333535513299868115*c_1\ 010_12^19 + 189160711547745758880444382/55375796333535513299868115*\ c_1010_12^18 + 1730132163971067568580445416/55375796333535513299868\ 115*c_1010_12^17 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